Chapter 10, Problem 98A

To determine

To Rank: Each interaction according to the work the boy does on the bench, from least to greatest, when a boy interacts with a bench.

Answer to Problem 98A

  $W_e=W_{{}_c}<W_b<W_a=W_d$$$

Explanation of Solution

Given:

The force given at each = 100 N (A), 100 N (B), mg (C), 100 N (D), 220 N (E).

Distances ( d ) = (5 m, in A), (5 m, in B), (0 m, in C), (5 m, in D), (0 m, in E).

Formula used:

  $W=F\cdot d$.$$

Calculation:

The work done is defined as the constant force multiplied with the displacement of an object/body.

Mathematically,

  $W=F\cdot d=Fd\cos \theta$$$

Substituting the values of force and displacement from A in work done equation.

  $W=100\times 5=500\text{ N}\cdot \text{m}$

From figure B.

  $W=100\cos 25\times 5\text{ = 453}\text{.15 N}\cdot \text{m }$$$

From figure C.

  $\begin{array}{l}W=m.g\times d\text{ N}\cdot \text{m}\\ W=20\text{ kg}\times 9.81{\text{ m/s}}^2\times 0\text{ N}\cdot \text{m}\\ W=0\end{array}$

From figure D.

  $W=100\times 5=500\text{ N}\cdot \text{m}$

From figure E.

  $W=220\times 0\text{ = 0 N}\cdot \text{m }$$$

Conclusion:

The work done is calculated for each interaction and ranked accordingly: $W_e=W_{{}_c}<W_b<W_a=W_d$